Published October 2018
| Version Submitted
Journal Article
Open
Entanglement in Non-local Games and the Hyperlinear Profile of Groups
Creators
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1.
University of Waterloo
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2.
California Institute of Technology
Abstract
We relate the amount of entanglement required to play linear system non-local games near-optimally to the hyperlinear profile of finitely presented groups. By calculating the hyperlinear profile of a certain group, we give an example of a finite non-local game for which the amount of entanglement required to play ϵ-optimally is at least Ω(1/ϵ^k), f or some k > 0. Since this function approaches infinity as ϵ approaches zero, this provides a quantitative version of a theorem of the first author.
Additional Information
© 2018 Springer Nature Switzerland AG. Received: 30 November 2017; Accepted: 10 June 2018; First Online: 02 August 2018. As mentioned in Introduction, we are grateful to Narutaka Ozawa for suggesting the use of the Connes embedding trick and the beautiful line of argument now incorporated in Sect. 5; this led to a substantial improvement in our results. The first author also thanks Martino Lupini for helpful discussions. The second author is supported by NSF CAREER Grant CCF-1553477, AFOSR YIP Award Number FA9550-16-1-0495, a CIFAR Azrieli Global Scholar award, and the IQIM, an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028).Attached Files
Submitted - 1711.10676.pdf
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Additional details
Identifiers
- Eprint ID
- 89964
- Resolver ID
- CaltechAUTHORS:20180926-132554192
Related works
- Describes
- https://arxiv.org/abs/1711.10676 (URL)
Funding
- NSF
- CCF-1553477
- Air Force Office of Scientific Research (AFOSR)
- FA9550-16-1-0495
- Canadian Institute for Advanced Research (CIFAR)
- Institute for Quantum Information and Matter (IQIM)
- NSF
- PHY-1125565
- Gordon and Betty Moore Foundation
- GBMF-12500028
Dates
- Created
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2018-09-26Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field